""" NAdamW Optimizer Based on simplified algorithm in https://github.com/mlcommons/algorithmic-efficiency/tree/main/baselines/nadamw Added multi-tensor (foreach) path. References for added functionality: Cautious Optimizers: https://arxiv.org/abs/2411.16085 Why Gradients Rapidly Increase Near the End of Training: https://arxiv.org/abs/2506.02285 """ import math from typing import List, Optional, Tuple import torch from torch import Tensor from ._types import ParamsT # Modified from github.com/pytorch/pytorch/blob/v1.12.1/torch/optim/adamw.py. class NAdamW(torch.optim.Optimizer): """ Implements NAdamW algorithm. See Table 1 in https://arxiv.org/abs/1910.05446 for the implementation of the NAdam algorithm (there is also a comment in the code which highlights the only difference of NAdamW and AdamW). For further details regarding the algorithm we refer to - Decoupled Weight Decay Regularization: https://arxiv.org/abs/1711.05101 - On the Convergence of Adam and Beyond: https://openreview.net/forum?id=ryQu7f-RZ Args: params: iterable of parameters to optimize or dicts defining parameter groups lr: learning rate betas: coefficients used for computing running averages of gradient and its square eps: term added to the denominator to improve numerical stability weight_decay: weight decay coefficient caution: enable caution corrected_weight_decay: apply corrected weight decay (lr**2 / max_lr) """ def __init__( self, params: ParamsT, lr: float = 1e-3, betas: Tuple[float, float] = (0.9, 0.999), eps: float = 1e-8, weight_decay: float = 1e-2, caution: bool = False, corrected_weight_decay: bool = False, maximize: bool = False, foreach: Optional[bool] = None, capturable: bool = False, ): if not 0.0 <= lr: raise ValueError(f'Invalid learning rate: {lr}') if not 0.0 <= eps: raise ValueError(f'Invalid epsilon value: {eps}') if not 0.0 <= betas[0] < 1.0: raise ValueError(f'Invalid beta parameter at index 0: {betas[0]}') if not 0.0 <= betas[1] < 1.0: raise ValueError(f'Invalid beta parameter at index 1: {betas[1]}') if not 0.0 <= weight_decay: raise ValueError(f'Invalid weight_decay value: {weight_decay}') defaults = dict( lr=lr, betas=betas, eps=eps, weight_decay=weight_decay, caution=caution, corrected_weight_decay=corrected_weight_decay, foreach=foreach, maximize=maximize, capturable=capturable, ) super().__init__(params, defaults) def __setstate__(self, state): super().__setstate__(state) state_values = list(self.state.values()) step_is_tensor = (len(state_values) != 0) and torch.is_tensor(state_values[0]['step']) if not step_is_tensor: for s in state_values: s['step'] = torch.tensor(float(s['step'])) for group in self.param_groups: group.setdefault('caution', False) group.setdefault('corrected_weight_decay', False) @torch.no_grad() def step(self, closure=None): """Performs a single optimization step. Args: closure (callable, optional): A closure that reevaluates the model and returns the loss. """ self._cuda_graph_capture_health_check() loss = None if closure is not None: with torch.enable_grad(): loss = closure() for group in self.param_groups: params_with_grad = [] grads = [] exp_avgs = [] exp_avg_sqs = [] state_steps = [] beta1, beta2 = group['betas'] for p in group['params']: if p.grad is None: continue params_with_grad.append(p) if p.grad.is_sparse: raise RuntimeError('NAdamW does not support sparse gradients') grads.append(p.grad) state = self.state[p] # State initialization if len(state) == 0: state['step'] = torch.tensor(0.) # Exponential moving average of gradient values state['exp_avg'] = torch.zeros_like(p, memory_format=torch.preserve_format) # Exponential moving average of squared gradient values state['exp_avg_sq'] = torch.zeros_like(p, memory_format=torch.preserve_format) exp_avgs.append(state['exp_avg']) exp_avg_sqs.append(state['exp_avg_sq']) state_steps.append(state['step']) nadamw( params_with_grad, grads, exp_avgs, exp_avg_sqs, state_steps, beta1=beta1, beta2=beta2, lr=group['lr'], weight_decay=group['weight_decay'], eps=group['eps'], caution=group['caution'], maximize=group['maximize'], capturable=group['capturable'], max_lr=self.defaults['lr'] if group['corrected_weight_decay'] else None, ) return loss def nadamw( params: List[Tensor], grads: List[Tensor], exp_avgs: List[Tensor], exp_avg_sqs: List[Tensor], state_steps: List[Tensor], foreach: Optional[bool] = None, capturable: bool = False, *, beta1: float, beta2: float, lr: float, weight_decay: float, eps: float, caution: bool, maximize: bool, max_lr: float, ) -> None: r"""Functional API that performs NAdamW algorithm computation. See NAdamW class for details. """ if not all(isinstance(t, torch.Tensor) for t in state_steps): raise RuntimeError( 'API has changed, `state_steps` argument must contain a list of' + ' singleton tensors') if foreach is None: try: # cannot do foreach if this overload doesn't exist when caution enabled foreach = not caution or 'Scalar' in torch.ops.aten._foreach_maximum_.overloads() except: foreach = False if foreach and not torch.jit.is_scripting(): func = _multi_tensor_nadamw else: func = _single_tensor_nadamw func( params, grads, exp_avgs, exp_avg_sqs, state_steps, beta1=beta1, beta2=beta2, lr=lr, weight_decay=weight_decay, eps=eps, caution=caution, maximize=maximize, capturable=capturable, max_lr=max_lr, ) def _single_tensor_nadamw( params: List[Tensor], grads: List[Tensor], exp_avgs: List[Tensor], exp_avg_sqs: List[Tensor], state_steps: List[Tensor], *, beta1: float, beta2: float, lr: float, weight_decay: float, eps: float, caution: bool, maximize: bool, capturable: bool, max_lr: Optional[float], ): for i, param in enumerate(params): grad = grads[i] if not maximize else -grads[i] exp_avg = exp_avgs[i] exp_avg_sq = exp_avg_sqs[i] step_t = state_steps[i] # Update step. step_t += 1 # Perform stepweight decay. wd_scale = lr if max_lr is None else lr ** 2 / max_lr param.mul_(1. - wd_scale * weight_decay) # Decay the first and second moment running average coefficient. exp_avg.mul_(beta1).add_(grad, alpha=1 - beta1) exp_avg_sq.mul_(beta2).addcmul_(grad, grad, value=1 - beta2) if capturable: step = step_t # 1 - beta1 ** step can't be captured in a CUDA graph, even if step is a CUDA tensor # (incurs "RuntimeError: CUDA error: operation not permitted when stream is capturing") bias_correction1 = 1 - torch.pow(beta1, step) bias_correction2 = 1 - torch.pow(beta2, step) step_size = lr / bias_correction1 step_size_neg = step_size.neg() bias_correction2_sqrt = bias_correction2.sqrt() # Only difference between NAdamW and AdamW in this implementation. # The official PyTorch implementation of NAdam uses a different algorithm. exp_avg = exp_avg.mul(beta1).add_(grad, alpha=1 - beta1) denom = (exp_avg_sq.sqrt() / (bias_correction2_sqrt * step_size_neg)).add_(eps / step_size_neg) if caution: # Apply caution as per 'Cautious Optimizers' - https://arxiv.org/abs/2411.16085 # FIXME not 100% sure if this remains capturable? mask = (exp_avg * grad > 0).to(grad.dtype) mask.div_(mask.mean().clamp_(min=1e-3)) exp_avg.mul_(mask) param.addcdiv_(exp_avg, denom) else: step = step_t.item() bias_correction1 = 1 - beta1 ** step bias_correction2 = 1 - beta2 ** step step_size = lr / bias_correction1 bias_correction2_sqrt = math.sqrt(bias_correction2) # Apply Nesterov. Only difference between NAdamW and AdamW in this implementation. # The official PyTorch implementation of NAdam uses a different algorithm. exp_avg = exp_avg.mul(beta1).add_(grad, alpha=1 - beta1) denom = (exp_avg_sq.sqrt() / bias_correction2_sqrt).add_(eps) if caution: # Apply caution as per 'Cautious Optimizers' - https://arxiv.org/abs/2411.16085 mask = (exp_avg * grad > 0).to(grad.dtype) mask.div_(mask.mean().clamp_(min=1e-3)) exp_avg.mul_(mask) param.addcdiv_(exp_avg, denom, value=-step_size) def _multi_tensor_nadamw( params: List[Tensor], grads: List[Tensor], exp_avgs: List[Tensor], exp_avg_sqs: List[Tensor], state_steps: List[Tensor], *, beta1: float, beta2: float, lr: float, weight_decay: float, eps: float, caution: bool, maximize: bool, capturable: bool, max_lr: Optional[float], ): if len(params) == 0: return if capturable: assert all( p.is_cuda and step.is_cuda for p, step in zip(params, state_steps) ), "If capturable=True, params and state_steps must be CUDA tensors." if maximize: grads = torch._foreach_neg(tuple(grads)) # type: ignore[assignment] grads = [torch.view_as_real(x) if torch.is_complex(x) else x for x in grads] exp_avgs = [torch.view_as_real(x) if torch.is_complex(x) else x for x in exp_avgs] exp_avg_sqs = [torch.view_as_real(x) if torch.is_complex(x) else x for x in exp_avg_sqs] params = [torch.view_as_real(x) if torch.is_complex(x) else x for x in params] # update steps torch._foreach_add_(state_steps, 1) # Perform stepweight decay wd_scale = lr if max_lr is None else lr ** 2 / max_lr torch._foreach_mul_(params, 1 - wd_scale * weight_decay) # Decay the first and second moment running average coefficient torch._foreach_mul_(exp_avgs, beta1) torch._foreach_add_(exp_avgs, grads, alpha=1 - beta1) torch._foreach_mul_(exp_avg_sqs, beta2) torch._foreach_addcmul_(exp_avg_sqs, grads, grads, 1 - beta2) if capturable: # TODO: use foreach_pow if/when foreach_pow is added bias_correction1 = [torch.pow(beta1, step) for step in state_steps] bias_correction2 = [torch.pow(beta2, step) for step in state_steps] # foreach_sub doesn't allow a scalar as the first arg torch._foreach_sub_(bias_correction1, 1) torch._foreach_sub_(bias_correction2, 1) torch._foreach_neg_(bias_correction1) torch._foreach_neg_(bias_correction2) # foreach_div doesn't allow a scalar as the first arg step_size = torch._foreach_div(bias_correction1, lr) torch._foreach_reciprocal_(step_size) torch._foreach_neg_(step_size) bias_correction2_sqrt = torch._foreach_sqrt(bias_correction2) # Only difference between NAdamW and AdamW in this implementation. # The official PyTorch implementation of NAdam uses a different algorithm. exp_avgs = torch._foreach_mul(exp_avgs, beta1) torch._foreach_add_(exp_avgs, grads, alpha=1 - beta1) exp_avg_sq_sqrt = torch._foreach_sqrt(exp_avg_sqs) torch._foreach_div_( exp_avg_sq_sqrt, torch._foreach_mul(bias_correction2_sqrt, step_size) ) eps_over_step_size = torch._foreach_div(step_size, eps) torch._foreach_reciprocal_(eps_over_step_size) denom = torch._foreach_add(exp_avg_sq_sqrt, eps_over_step_size) if caution: # Apply caution as per 'Cautious Optimizers' - https://arxiv.org/abs/2411.16085 masks = torch._foreach_mul(exp_avgs, grads) masks = [(m > 0).to(g.dtype) for m, g in zip(masks, grads)] # capturable? mask_scale = [m.mean() for m in masks] torch._foreach_maximum_(mask_scale, 1e-3) #torch._foreach_clamp_min_(mask_scale, 1e-3) torch._foreach_div_(masks, mask_scale) torch._foreach_mul_(exp_avgs, masks) torch._foreach_addcdiv_(params, exp_avgs, denom) else: bias_correction1 = [1 - beta1 ** step.item() for step in state_steps] bias_correction2 = [1 - beta2 ** step.item() for step in state_steps] step_size = [(lr / bc) * -1 for bc in bias_correction1] bias_correction2_sqrt = [math.sqrt(bc) for bc in bias_correction2] # Apply Nesterov. Only difference between NAdamW and AdamW in this implementation. # The official PyTorch implementation of NAdam uses a different algorithm. exp_avgs = torch._foreach_mul(exp_avgs, beta1) torch._foreach_add_(exp_avgs, grads, alpha=1 - beta1) exp_avg_sq_sqrt = torch._foreach_sqrt(exp_avg_sqs) torch._foreach_div_(exp_avg_sq_sqrt, bias_correction2_sqrt) denom = torch._foreach_add(exp_avg_sq_sqrt, eps) if caution: # Apply caution as per 'Cautious Optimizers' - https://arxiv.org/abs/2411.16085 masks = torch._foreach_mul(exp_avgs, grads) masks = [(m > 0).to(g.dtype) for m, g in zip(masks, grads)] mask_scale = [m.mean() for m in masks] torch._foreach_maximum_(mask_scale, 1e-3) #torch._foreach_clamp_min_(mask_scale, 1e-3) torch._foreach_div_(masks, mask_scale) torch._foreach_mul_(exp_avgs, masks) torch._foreach_addcdiv_(params, exp_avgs, denom, step_size)